Today in Precalculus Go over homework Notes: Log Functions(need a calculator) –Graphing –Applications Homework

Extrema: Asymptotes: D: ( 0,∞) R: ( – ∞, ∞ ) x-int: (1, 0) continuous incr: ( 0, ∞) no symmetry unbounded D: R: intercepts continuity Incr. / decr. Symmetry Boundedness Extrema: none Asymptotes: x = 0 End Behavior: Graphing Log Functions

Transformations Describe how to transform the graph of the f(x) = ln x into the graph of the given function. Sketch by hand. a.) g(x) = ln (– x) + 2 reflect over y-axis shift up 2 original points: (1,0) & (2.7,1)

Transformations Describe how to transform the graph of the f(x) = log x into the graph of the given function. Sketch by hand. b.) h(x) = -2 log(-x) +1 reflect over y-axis reflect over x-axis vertical stretch 2 shift up 1 original points: (1,0) & (10,1)

Applications f(t) = 75 – 6ln(t + 1) for 0 ≤ t ≤ 12 where t is time in months What was the average score on the original exam (t = 0)? f(0) = 75 – 6ln(0+1) = 75 – 6(0) = 75 After six months, what was the average score? f(6) = 75 – 6ln(6+1) = After ten months, what was the average score? f(10) = 75 – 6ln(10+1) =

Application tf(t)

Sound Intensity A log model used for measuring the intensity of sound. I: intensity I 0 = watts per square meter

Example Find the level of sound if the intensity is 10 -8

Homework Page 308: 41-44, 47, 49, 50, 59, 60 Quiz: Friday, December 18